Optimal plug-in electric vehicle charging with schedule constraints

This paper proposes a decentralized algorithm that allows a group of Plug-in Electric Vehicles (PEVs) to arrive at an optimal strategy to charge their batteries during the day. By communicating repeatedly with an energy coordinator, the PEVs adjust their battery-charging plans by means of a price-feedback signal that accounts for the aggregated demand. The algorithm allows PEVs to adjust their plan simultaneously while respecting schedule constraints at every iteration. The collective strategy is optimal in that it minimizes the overall price of the supplied energy and leads to an off-peak utilization of the grid. The algorithm is proven to converge to a solution by means of nonlinear analysis tools of discrete-time systems. In order to show convergence, we present a refinement of the LaSalle invariance principle for discrete-time systems. Simulations demonstrate the proficiency of the algorithm in two particular scenarios.